ORIGINAL RESEARCH published: 31 May 2019 doi: 10.3389/fphys.2019.00473 Thermodynamic Efficiency of Somatic Exocytosis of Serotonin Paula Noguez 1 , J. Miguel Rubí 2 and Francisco F. De-Miguel 3* 1 Instituto de Fisiología Celular-Neurociencias, Universidad Nacional Autónoma de México, Mexico City, Mexico, 2 Facultat de Física, Universitat de Barcelona, Barcelona, Spain, 3 Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Mexico City, Mexico Through somatic exocytosis neurons liberate immense amounts of transmitter molecules that modulate the functioning of the nervous system. A stream of action potentials triggers an ATP-dependent transport of transmitter-containing vesicles to the plasma membrane, that ends with a large-scale exocytosis. It is commonly assumed that biological processes use metabolic energy with a high thermodynamic efficiency, meaning that most energy generates work with minor dissipation. However, the intricate ultrastructure underlying the pathway for the vesicle flow necessary for somatic exocytosis challenges this possibility. To study this problem here we first applied thermodynamic theory to quantify the efficiency of somatic exocytosis of the vital transmitter serotonin. Then we correlated the efficiency to the ultrastructure of the transport pathway of the vesicles. Exocytosis was evoked in cultured Retzius neurons of the leech by trains of 10 impulses delivered at 20 Hz. The kinetics of exocytosis was quantified from the gradual fluorescence increase of FM1-43 dye as it became incorporated into vesicles that underwent their exo-endocytosis cycle. By fitting a Edited by: Christoph Fahlke, model of the vesicle transport carried by motor forces to the kinetics of exocytosis, Julich Research Centre, Germany we calculated the thermodynamic efficiency of the ATP expenses per vesicle, as the Reviewed by: power of the transport divided by total energy ideally produced by the hydrolysis of Ulrich Zachariae, ATP during the process. The efficiency was remarkably low (0.1–6.4%) and the values University of Dundee, United Kingdom Delany Torres-Salazar, formed a W-shape distribution with the transport distances of the vesicles. Electron National Institutes of Health (NIH), micrographs and fluorescent staining of the actin cortex indicated that the slopes of United States the W chart could be explained by the interaction of vesicles with the actin cortex *Correspondence: Francisco F. De-Miguel and the calcium-releasing endoplasmic reticulum. We showed that the application of ffernand@ifc.unam.mx thermodynamic theory permitted to predict aspects of the intracellular structure. Our results suggest that the distribution of subcellular structures that are essential for somatic Specialty section: This article was submitted to exocytosis abates the thermodynamic efficiency of the transport by hampering vesicle Membrane Physiology and Membrane mobilization. It is remarkable that the modulation of the nervous system occurs at the Biophysics, expenses of an efficient use of metabolic energy. a section of the journal Frontiers in Physiology Keywords: somatic exocytosis, extrasynaptic, serotonin, thermodynamic efficiency, vesicle transport, kinesin, Received: 08 November 2018 myosin, leech Accepted: 04 April 2019 Published: 31 May 2019 Citation: INTRODUCTION Noguez P, Rubí JM and De-Miguel FF (2019) Thermodynamic Efficiency of Extrasynaptic exocytosis, namely the release of transmitters and peptides from the neuronal soma, Somatic Exocytosis of Serotonin. dendrites, and axons, is a source of modulators of the activity of the nervous system (De-Miguel and Front. Physiol. 10:473. Fuxe, 2012; De-Miguel and Nicholls, 2015). Most low molecular weight transmitters and different doi: 10.3389/fphys.2019.00473 peptides are released extrasynaptically by exocytosis (for review see Trueta and De-Miguel, 2012). Frontiers in Physiology | www.frontiersin.org 1 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis Molecules released in this manner diversify the responses of the cytoarchitecture of the transport pathway, since electron neural circuits to a given stimulus by integrating the activity of micrographs contain endoplasmic reticulum and mitochondria neurons, glia and capillaries (Fuxe et al., 2007; Rozanski et al., -which are engines for somatic exocytosis- often invading the 2012; Hirasawa et al., 2015; Newman, 2015). transport pathway of the vesicles (Trueta et al., 2004, 2012; De- The mechanism for extrasynaptic exocytosis is substantially Miguel et al., 2012). In addition, the actin cortex at rest prevents different from that for release at synapses and similar to the vesicle transport, but after the onset of electrical activity turns the mechanism for exocytosis from endocrine cells. Somatic into a component of the transport system by binding to myosin exocytosis involves a multi-regulated sequence of serial and motors (Wang and Hatton, 2006; Tobin and Ludwig, 2007). parallel reactions that couple excitation with exocytosis (Ludwig Such observations raised the possibility that somatic exocytosis and Stern, 2015; Del-Bel and De-Miguel, 2018). Vesicles -usually operates under low thermodynamic efficiency, opposing to the large and electrodense (see Trueta and De-Miguel, 2012) filled common assumption that biological processes make a high with signaling molecules, rest far from the plasma membrane. efficiency use of their metabolic energy. Theoretically, when Bursts of electrical activity evoke a transmembrane calcium entry friction forces hamper the work, a fraction of the energy that triggers calcium release from the endoplasmic reticulum dissipates in the form of heat, reducing the thermodynamic (review see Trueta and De-Miguel, 2012; Del-Bel and De-Miguel, efficiency of the process. For this reason, measurements of the 2018). The calcium wave induces an increase of cytosolic ATP amount of energy provide only a partial story; it is also necessary that triggers the vesicle transport by the activation of molecular to estimate how efficiently the energy is used. This focal problem motors (Nicholls et al., 2003; Llorente-Folch et al., 2013; Rueda was studied here by making use of the advantages of the well- et al., 2014; Del-Pozo and De-Miguel, in preparation). Exocytosis known somatic exocytosis of serotonin by the Retzius neuron of starts as vesicles arrive at the plasma membrane (De-Miguel and the leech. Trueta, 2005). Calculations of the ATP expenses per vesicle fusing The large (∼70 µm) soma of a Retzius neuron stores serotonin (ATPves ) made by applying thermodynamic theory to the kinetics in astronomic numbers of 100 nm diameter electrodense vesicles of somatic exocytosis of serotonin, unveiled that the amount of (Coggeshall, 1972). At rest or following electrical stimulation ATPves has a W-shape dependence on the transport distance of with trains of 10 action potentials at 1 Hz (a frequency similar to the vesicles (De-Miguel et al., 2012). This relationship may reflect the spontaneous firing of serotonergic neurons), vesicles remain FIGURE 1 | Mechanism for somatic exocytosis in the Retzius neuron. (A) Schematic representation of the vesicle transport system. The scheme incorporates findings from this study. Vesicle clusters rest at variable distances from the plasma membrane. More than one cluster can be attached to the same microtubule (mt) bundle by kinesin motors (km). Internal clusters (red) lay across the actin cortex. The transport of vesicle clusters depends on four forces: the motor forces (fmot ), elastic forces (fel ), friction forces (ff ), and random forces (fr ). At rest, these forces are in equilibrium. The motor forces are microtubule- and kinesin-dependent (De-Miguel et al., 2012). Electrical stimulation produces a cascade of calcium-dependent events that activate the motor forces. Vesicle clusters are transported to the plasma membrane along a distance (d), at a velocity (v = d/t). Peripheral clusters (green) rest immersed in the actin cortex at the time of stimulation, flanked by two layers of endoplasmic reticulum (er1 , er2 ). Inside the actin cortex, myosin motors (mym) add to kinesin motors to transport the vesicle clusters to the plasma membrane (pm). The reduced number of vesicles as clusters approach the plasma membrane seems to obey a continuous vesicle detachment and transport to the plasma membrane (Leon-Pinzon et al., 2014). Fusion of these vesicles (arrowhead) produces the constitutive release of serotonin that permits the large-scale exocytosis when whole clusters arrive at the plasma membrane in response to electrical stimulation. (B) Biophysical parameters measured from the FM1-43 kinetics upon electrical stimulation of exocytosis. The green segment is the contribution of a peripheral cluster; the red segment is the contribution of an internal cluster. The latency to the onset of release contains information on the distance and velocity (t = d/v) of the vesicle transport. The J value is the flux of vesicles (vesicles fused per second). The no values are the number of vesicles that fused per vesicle cluster. Frontiers in Physiology | www.frontiersin.org 2 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis clustered at variable distances from the plasma membrane and Stimulation and Detection of Exocytosis exocytosis does not occur (Figure 1; De-Miguel et al., 2012). Exocytosis was quantified from the fluorescence increases By contrast, the same number of action potentials evoked at a produced by the incorporation of FM1-43 (2 µM; Molecular high 20 Hz frequency triggers the massive transport of vesicle Probes) by the vesicles that undergo fusion and endocytosis (Betz clusters to the plasma membrane and the large-scale exocytosis. and Bewick, 1993). Vesicle fusion permits the dye to enter the Within the following hundreds of seconds, tens of thousands of vesicles and stain their internal membrane. Endocytosis keeps the vesicles distributed in ∼90 clusters will discharge their content dye inside the vesicle. Therefore, each vesicle fusion contributes from different parts of the soma (Trueta et al., 2003; De-Miguel with a step to the fluorescence in the release site. We have et al., 2012). The large-scale exocytosis is sustained for long previously shown that the large-scale exocytosis from vesicles periods in absence of further transmembrane calcium entry, by arriving in a cluster lasts for hundreds of seconds, depending the serotonin that has been released (Leon-Pinzon et al., 2014). on the number of vesicles in the distance and the velocity of Activation of serotonin autoreceptors evoke an intracellular IP3- the transport. Upon endocytosis, the stained vesicles accumulate dependent release of calcium from the endoplasmic reticulum near the plasma membrane without being recycled to the adjacent to the plasma membrane. This localized calcium releasable pool. Instead, they get packed forming multivesicular elevation maintains exocytosis until the fusion of the last vesicles bodies that are later transported to the perikaryon (Trueta et al., in the clusters (Leon-Pinzon et al., 2014). It is common that a 2012). Therefore, the gradual increase of fluorescence reflects second and larger cluster of vesicles arrives at the same release site accurately the kinetics of exocytosis; the plateau is reached once producing a second bulk of exocytosis (De-Miguel et al., 2012; all the electrodense vesicles in the cluster have fused and the Leon-Pinzon et al., 2014). Figure 1 recapitulates the elementary intensity of fluorescence indicates the number of vesicles that aspects of this mechanism. fused (De-Miguel et al., 2012). If any stained vesicle fuses again In this study we applied a thermodynamic theoretical the amount of fluorescence does not increase because the vesicle approach to calculate the efficiency of somatic exocytosis of is already stained. serotonin. As the reporter of exocytosis we used the fluorescence Stimulation of exocytosis consisted of trains of 10 action increase of FM1-43 dye, which stains the inside of vesicles that potentials produced by intracellular injection of 10 ms current undergo their exocytosis/endocytosis cycle (Betz et al., 1992; pulses at 20 Hz delivered every 2 min. The amplitude of the De-Miguel et al., 2012). A mathematical approach applied to current pulses was adjusted in every neuron between 5 and 8 the kinetics of exocytosis permitted to calculate the transport nA, to guarantee that each pulse in the train produced one distance, velocity and power of the whole process of somatic action potential. The intracellular voltage was recorded using a exocytosis from individual release sites. By incorporating new Getting pre-amplifier operating in bridge balance mode. In eight experimental data to the model fittings, we improved our other neurons the actin cortex was uncoupled by incubation previous estimates of the ATP expenses per vesicle fused with 1 µM cytochalasin D (Sigma-Aldrich) for 30 min at 18◦ C (ATPves ). The thermodynamic efficiency of the ATPves expenses before stimulation. was calculated from the work in the presence of friction forces, Individual neurons were focused on their equator with a divided by the ideal energy generated by the ATP cleavage. The Nikon Eclipse TE 200 inverted microscope using a Nikon 100x thermodynamic efficiency along the traveling distance of the oil immersion objective (NA 1.40). FM1-43 was excited at 488 nm vesicles was correlated with the ultrastructure of the transport and its fluorescent emission was measured at 543 nm. Images pathway, analyzed from electron micrographs, and fluorescent were taken every 2 s with a cooled CCD camera (IMAGO, Till staining of the actin cortex. Vision, Germany) at a 640 × 480-pixel resolution. Processing was made offline by using TILLvisION software. The fluorescence measurements were made by linear MATERIALS AND METHODS interpolation, after non-specific fluorescence in each sequential image was subtracted from the intensity of the membrane. The Ethics Statement area of release was estimated from the length of membrane in Animal research was approved by the Animal Committee of the which fluorescence increased, by assuming that it was circular Instituto de Fisiología Celular, Universidad Nacional Autónoma (De-Miguel et al., 2012). This number served as a reference for de México. the model estimates of the number of vesicles (see Equation 1). Isolation and Culture of Neurons Exclusion Criteria Experiments were made using Retzius neurons of the medicinal Neurons commonly moved after electrical stimulation. leech Hirudo sp. For experiments with FM1-43, neurons Therefore, the focus of each spot in the time series analysis were individually isolated by suction through a glass pipette had to be confirmed from a z axis scanning of the neurons at after an enzyme treatment (Dietzel et al., 1986) and plated the end of the experiment. Only fluorescent spots that remained in glass-bottom culture dishes coated with concanavalin-A in focus during the whole experiment or that could be aligned (Sigma, St. Louis, MO). The culture medium was L-15 (Sigma) digitally were included in the analysis. Clusters extending for supplemented with 6 mg/mL glucose, 0.1 mg/mL gentamycin and more than 1 µm of membrane length were excluded to avoid out- 2% fetal bovine serum (Gibco, Gaithersburg, MD). Experiments of-focus fluorescent emissions due to large numbers of vesicles were made at 18◦ C after 1–3 days in culture. (De-Miguel et al., 2012). For these reasons, we eliminated Frontiers in Physiology | www.frontiersin.org 3 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis from our analysis a vast number of observations. However, the data from nine different neurons in which subsequent uncorrelated clusters of vesicles arrived at the same spot were a fair representation of the population. Quantitative Analysis of Exocytosis The model was developed based on the kinetic properties of the FM1-43 fluorescence increases during exocytosis (Figure 2). A full account of the theoretical development of the model is presented in De-Miguel et al. (2012). In brief, the fluorescence kinetics F(t) is proportional to the flux J ves of vesicles arriving at the plasma membrane. The process of exocytosis is orders of magnitude faster than the speed of the vesicle transport. Therefore, the flux reflects the transport and can be defined as the number of vesicles fusing per second at an area A of the plasma membrane, according to: Z t F(t) = F0 + Ab Jves (d, t ′ )dt ′ (1) 0 In Equation (1), F0 is the basal fluorescence produced by the interaction of the fluorescent dye with the extracellular layer of the plasma membrane; b is a proportionality factor relating the amount of fluorescence contributed by each vesicle. This proportionality stems from the fact that the internal FIGURE 2 | Kinetics of the large-scale exocytosis as measured from the fluorescence increases of FM1-43. (A) Superimposition of the FM fluorescence membrane surface of the population of electrodense vesicles can (Fluo) kinetics of eight representative spots from an equal number of neurons. be considered constant. The parameter “t” is the time, while “d” Stimulation occurred at t = 0. A subsequent stimulation train was delivered is the transport distance from the center of mass of the resting every 2 min. Fluorescence is plotted as the percentage increase over the cluster to the plasma membrane. The distance was estimated baseline. Subsequent sigmoidal increases appear in most kinetics, with each reflecting exocytosis from a subsequent vesicle cluster. (B) Treatment of by the model and was correlated with distances measured from neurons with cytochalasin D that uncouples the actin cortex delayed and electron micrographs of neurons stimulated with 1 Hz trains of reduced the fluorescence increases in response to stimulation and abolished impulses (De-Miguel et al., 2012). The plateau of the fluorescence the second sigmoidal fluorescence increase. The plot superimposes six increase indicates the total the number of vesicles (n0 ) that kinetics from an equal number of neurons. Note the difference in the fused (Figure 1B). The parameters used in the model are in fluorescence scale bars between (A,B). Table 1. The contribution of the distance, velocity and number of vesicles to the kinetics of fluorescence are presented schematically in Figure 1. As shown also in Figure 1, the flux of vesicles, Jves , depends on We consider that the vesicle motion toward the cell membrane four forces. The first two are a frictional force due to the resistance is unidimensional and can be described in terms of the distance opposed by the medium to the vesicle motion and a random force coordinate. Therefore, Jves depends on the friction and motor produced by thermal agitation. These two forces produce the forces plus the contribution of diffusion, where Jves = ρvves and Brownian motion of the vesicles at the experimental temperature. vves = β −1 F. Then Jves can also be expressed as: The third force is elastic and confines the individual vesicles in a cluster. These forces are considered harmonic because the vesicle ∂ρ Jves = −D + β −1 ρF (4) displacements they produce are small. This assumption simplifies ∂x the model. The fourth force is used by the motors to carry the vesicle clusters plus mitochondria at an average velocity “vves ” where the term −D ∂ρ ∂x accounts for diffusion, with D the being (Svoboda and Block, 1994; Schnitzer and Block, 1997). The Force the diffusion coefficient, and the second term is the product of of the motor and the elastic forces acting together on the vesicles the friction (β −1 ρ) and the motor (F) forces, due to the effect of can be defined as: the driving force (De-Miguel et al., 2012). F = fel + fmot = ω2 (d − vt) (2) These forces are modeled by a linear function of the position, which corresponds to a harmonic force. Harmonic forces yield in Where ω is the characteristic frequency at which the elastic forces general an oscillatory motion in which the velocity of the particle confine the vesicles, as described by: decreases until it vanishes at a certain point, and then increases in the opposite direction. In this case the harmonic force acts only during forward motion. Therefore, that sole force can model the r k ω= (3) main movement of the vesicles to the plasma membrane. m Frontiers in Physiology | www.frontiersin.org 4 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis TABLE 1 | Definition of the parameters used in the model. TABLE 2 | Ranges of parameter values contributing to the vesicle transport. Symbol Definition Dimensions Cluster Peripheral Internal A Area of a release site measured from the L2 η0 98–490 52–930 diameter of the fluorescence increase d (µm) 0.6–2.1 1.9–6.2 ATPves Number of ATP molecules hydrolyzed per _ v (nm/s) 15.0–95.0 11.5–60.0 vesicle fused. Jves (ves/sec) 0.2–4.0 0.9–10.33 β Dimensionless constant referring to the _ Elastic force (N × 10−11 ) 1.2–4.2 3.8–12.0 fluorescence increase per vesicle fused (0.6–4.1) (2.2–24.2) d Transport distance of vesicle clusters measured L Motor force (N × 10−10 ) 1.2–6.0 1.8–4.7 from the center of mass of the cluster to the (0.6–4.4) (1.4–3.5) plasma membrane ATPves 10.9–49.4 13.6–260 1G Gibb’s free energy ML2 T−2 (3.4–73.0) (0.4–25.1) 1GATP Gibb’s free energy of ATP hydrolysis ML2 T−2 Efficiency (%) 0.2–6.4 0.1–1.9 F0 Baseline value of the fluorescence intensity a.u. F(t) Fluorescence as a function of time a.u. Data in red are the estimates calculated in this study; data in parenthesis are from our previous study (De-Miguel et al., 2012). F Force exerted by the motors MLT−2 ff Friction forces per mass unit LT−2 fr(t) Random forces due to thermal agitation per LT−2 mass unit The 1GATP value was 5.4 × 10−20 Joules (Alberty and Goldberg, fel Elastic forces per mass unit LT−2 1992), and n0 is the number of vesicles that fused (see Equation fmot Molecular motor force per mass unit LT−2 1). Table 2 compares the data obtained for the elastic and motor Fv Power of the large-scale exocytosis ML2 T−3 forces, and for the ATPves expenses reported here and in our previous study (De-Miguel et al., 2012). Table 2 shows that the Jves Current density of vesicles L−2 T−1 ATPves values presented here remained within similar orders of κ Elastic constant of the cytoskeleton MT−2 magnitude than those previously reported. m Mass M η Thermodynamic efficiency _ Thermodynamic Efficiency no Number of vesicles per cluster _ Since energy dissipation due to the presence of frictional forces is r Rate constant of ATP hydrolysis T−1 expected to occur in a non-ideal transport by living neurons, we v Average velocity of vesicle cluster transport LT−1 used the classical definition of efficiency as the ratio between the ω Characteristic frequency of the elastic force T−1 ideal and the lost work and applied as in De Groot and Mazur W Work of the large-scale exocytosis ML2 T−2 (1969), later applied to analyze the efficiency of the calcium ATPase by Lervik et al. (2012). Wideal − Wlost η= (7) Improved Estimates of ATP Consumption Wideal The work that moves the vesicle cluster-mitochondria complex along a certain distance equals the change in free energy: The Wideal is the given by: Wideal = −r1r G (8) Wtot = k(d2 − dvt) = 1Gprocess (5) Where r is the force-related rate of ATP cleaved by the molecular In our previous calculations, the elastic (k) constant value of motors. The kinetics of force generation of molecular motors the molecular motors was a free parameter in the model. For are consistent with a two-step reaction (Higuchi et al., 1997). such reason there were variations in its predicted value from one The binding of ATP has a rate constant that depends on the release site to another (De-Miguel et al., 2012). In this study, we concentration and therefore its units are µM−1 ·s−1 ; a second fed the model with a unique k = 0.027 pN/nm value measured rate constant r accounts for the force generation used here, and experimentally by Bruno et al. (2011). has s−1 units (Higuchi et al., 1997). The r value related to the Equation (6) expresses the total amount of energy provided force generation is the one that matters for our estimates, since by the cleavage of ATP that is necessary under ideal conditions, according to De Groot and Mazur (1969, Equation 10 of Chapter to transport a vesicle cluster for a certain distance without X), it relates the reaction rate to the production of entropy. This dissipation. Due to the heterogeneity of the vesicle cluster definition is adequate to calculate the efficiency since the entropy sizes, the energy is expressed as the number of ATP molecules production related to thermal dissipation. As in our previous hydrolyzed per vesicle fused (ATPves ) by dividing the numerator equation, 1r G is the Gibbs free energy of the ATP cleavage. by the number of vesicles in the cluster n0 : The work lost (Wlost ) can be obtained from the Gouy-Stodola theorem in Equation (7) (see Kjelstrup et al., 2010): 1Gprocess ATPves = (6) Wlost = Tσ (9) n0 1GATP Frontiers in Physiology | www.frontiersin.org 5 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis where T is the constant temperature of the surroundings of the procedure was preferred over minimum square methods because system and σ is the production of entropy that accounts for the sigmoidal functions with two crossovers became smoothed in thermal dissipation. In our case, the energy is dissipated during abrupt parts of curves that had strong contributions by the motor the transport of vesicles and in the process of the ATP hydrolysis activity. A previous account on the quality of the fittings and at a rate given by: the effects of varying the values of the free parameters has been presented in De-Miguel et al. (2012). Tσ = −r1G − Jves 1µves (10) The data sets relating the ATPves expenses and the efficiency vs. distance presented in Figure 6 were fitted to empirical This expression was derived according to energy conservation polynomial functions to underscore the W-shape of the charts. along the transport path; 1µves in a previous paper was an The order of the polynomials was adjusted to obtain the best electroneutral exchange of ions by the calcium ATPase (22), R2 correlation values. The polynomial functions in our previous and here it relates to the force F of the motors. We also study had better fittings; data of peripheral clusters were fitted considered a negligible thermal driving force (Lervik et al., 2012). by a third-order polynomial function with R2 = 0.92. Likewise, This expression was also used by Caplan and Essig (1999), the fitting quality of the internal cluster data was R2 = 0.83. who considered the isothermal case and the linear regime of The reason for the lower quality of the fittings presented here proper pathways. is the absence of data in the distance ranges of the minimum The efficiency η of vesicle exocytosis can be given in terms of peaks (see Figure 6A). However, the polynomial fittings had no measurable quantities as: other intention than to give numeric support to the clear W- shaped trend of the data. In any case, due to the calculation −r1G − Tσ Jves 1µves improvements already described, we consider that the data sets η = = (11) −r1G −r1G in this study are more precise. The numerator of this fraction involves the flux of particles Staining of the Actin Cortex Jves and the chemical potential difference 1µves between the The actin cortex was measured from fluorescent stainings made initial and the final position of the vesicles, which corresponds by use of phalloidin coupled to a fluorescent probe. Neurons were to a force. Since in the experiments we follow the trajectories of fixed right after stimulation with CytoSkelFix (Cytoskeleton) for the vesicles, the numerator that corresponds to the work applied 4 min at −20◦ C and permeabilized for 30 min with phosphate- to the vesicles to move with a velocity vves is given by the product buffer saline (PBS) solution containing 0.3% Triton X-100. SFB Fves vves . The efficiency is then: (10%) was added as a blocker for 2 days, during which the preparations were maintained at 4◦ C. Actin was stained by Fves vves η = (12) incubation for 30 min at 37◦ C with phalloidin coupled to Alexa- r|1G| fluor 488 (0.16 µM, Invitrogen). Controls incubated in parallel without phalloidin were devoid of any staining. where Fves is the sum of elastic and motor forces given in Observations of fluorescence made using an Olympus Equation (2). Fluoview FV1000 upright confocal scanning microscope The efficiency per vesicle was calculated by dividing by the equipped with a 60X oil immersion objective (1.45 NA). Images number of vesicles (n0 ) in the cluster. were stored digitally using Fluoview 3.1 software (Olympus). The Fves vves thickness of the actin cortex was measured from digital images η= (13) using ImageJ software (NIH, USA). n0 r|1GATP | The rate constant r of the force generated by the ATP hydrolysis Electron Microscopy for kinesin motors is <100–300 s−1 (Higuchi et al., 1997; Cross, Neurons in isolated ganglia were fixed right after stimulation with 2004). A similar range of values has been measured for myosin 10 trains of 10 impulses at 1 or 20 Hz, delivered at 10 s intervals. motors (Johnson and Taylor, 1978; De La Cruz et al., 1999). The procedure to obtain thin (70–100 nm) sections for electron Therefore, the 100 s−1 value used here may account for either micrographs of Retzius cells were as in Kuffler et al. (1987). motor type acting separately and with non-additive effects. Sections were photographed in a JEOL 1010 electron microscope (JEOL USA Inc.). Curve Fitting and Statistical Analysis The kinetics of exocytosis of 19 release sites obtained from six RESULTS neurons were fitted to the mathematical model, as in De-Miguel et al. (2012; see Figure 5). The traveling distance and number Kinetics of Somatic Exocytosis of vesicles were limited by the ranges of values determined Electrical stimulation of Retzius neurons with 20 Hz trains previously from electron microscopy (De-Miguel et al., 2012). produced FM1-43 fluorescence spots at the neuronal surface In this way we reduced the possible combinations of values (Trueta et al., 2003). In this experimental situation each release estimated by the model and reduced the error in the fittings. site develops a fluorescent spot upon the subsequent fusion The data were fitted manually by using our own routines made of electrodense vesicles. A first sigmoidal fluorescence increase in MATLAB software (MathWorks, Massachusetts, USA). This (Figure 2A) reflects the fusion of vesicles forming a cluster that Frontiers in Physiology | www.frontiersin.org 6 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis rested at distances <2.0 µm from the plasma membrane (De- This experiment shows that the actin cortex has a sophisticated Miguel et al., 2012). Such clusters are named “peripheral” and contribution to somatic exocytosis. data are presented as green symbols (Figure 2B). A second sigmoidal increase in the same spot is due to fusion of vesicles The Rate of Vesicle Fusion Reflects the in clusters that traveled from more internal sites (see De-Miguel Transport Conditions et al., 2012). These clusters are called “internal,” and data are The calculations of the efficiency depended on the correct represented with red symbols (Figure 2B). measure of the flux of vesicles (J ves ; see Equations 1 and 4 The model fittings predicted that 52–930 vesicles per cluster in the Methods section), indirectly representing the rate of became fused in the 19 clusters analyzed from 10 neurons. There exocytosis. For this reason, it was necessary to demonstrate was no correlation between the number of vesicles, the distance, that the area of membrane did not limit exocytosis. This or the velocity of pairs of clusters arriving subsequently at the possibility was confirmed by correlating J ves with the number same release site (R2 ≤ 0.4 for all cases). For example, in a release of vesicles that fused. The J ves values ranged from 0.2 to 5.2 site the peripheral cluster contained 95 vesicles that traveled vesicles per second in the 19 clusters studied and had a linear along 0.6 µm at 70 nm/s, whereas the internal cluster contained relationship (R2 =0.85) with the area of release (Figure 3A). For 262 vesicles that traveled along 4.1 µm at 12 nm/s; in other release internal clusters the relation was sublinear with a 0.76 exponent site the peripheral cluster also had 95 vesicles that traveled along (R2 = 0.88). The deviation from linearity occurred when the 0.6 µm at 59 nm/s, but the internal cluster contained 675 vesicles number of vesicles per cluster was above 600. Such large clusters that traveled along 2.7 µm at 18 nm/s. In a third release site may have encountered major constrains in their traveling path, as the peripheral cluster was larger than the internal, however both will be confirmed below. However, the large clusters can extend traveled at the same 30 nm/s velocity. Data of the pairs of clusters over wide areas of membrane, as seen in electron micrographs can be seen in Figure 10. (Trueta et al., 2004). Therefore, we consider that the J ves values It was previously shown that uncoupling microtubules reflect accurately the transport velocity of the vesicle clusters. In by addition of colchicine to the neurons abolishes somatic support to this, Figure 3B shows that the efficiency of the ATP exocytosis, most likely by uncoupling the actin-mediated expenses was uncorrelated with the J ves values. transport (De-Miguel et al., 2012). In addition, the actin cortex in neurons and secretory cells imposes a barrier for the transport ATP-Dependence of the Thermodynamic at rest, but electrical activity in the presence of myosin turns the Efficiency actin cortex to an active transporter (Vitale et al., 1995; Lang The efficiency of the ATPves expenses of peripheral clusters et al., 2000; Oheim and Stühmer, 2000; Giner et al., 2005; Tobin spanned within more than one logarithmic unit from values as and Ludwig, 2007; Gutiérrez and Gil, 2011; Torregrosa-Hetland low as 0.2% for the smallest 11 ATPves value. From there, the et al., 2011). For its potential friction-generating qualities, we efficiency increased to its largest 6.4% value when the ATPves uncoupled the actin cortex to test its contribution to the ATP cost was 49 molecules (Figure 4). The intermediate data were expenses and efficiency of the transport. Pre-incubation of six described by a supralinear relationship. The 1.9 potency slope neurons with cytochalasin D in the bathing solution produced (R2 = 0.7) is consistent with the possible incorporation of a that in all but one case (n = 8 clusters from 6 neurons), second type of motor, presumably myosin coupled to the actin the latency to the onset of exocytosis was increased from cortex. This addition could increase the efficiency of ATPves 50–80 s to ∼300 s. In addition, the amplitude of the plateau expenses by incorporating the characteristic longer steps per fluorescence was reduced to values corresponding to 40–107 ATP molecule of myosin motors (Kohler and Rohrbach, 2015). vesicles fused (Figure 2B). It can also be seen that in all but The internal vesicle clusters were distributed within an efficiency one case the fluorescence increase lacked the second sigmoidal. range from 0.1 to 1.9% and a large range of ATPves cost of 14 to FIGURE 3 | The thermodynamic efficiency of the ATP per vesicle fused was independent from the rate of vesicle fusion (Jves ). (A) The Jves values related linearly to the number of vesicles in peripheral clusters (green), and with a 0.76 exponent to the number of vesicles of internal clusters (red; for explanation see text). (B) The efficiency did not correlate with the rate of fusion of internal or external clusters (black lines), respectively. The equations giving the best fit to the data and the significance levels are presented. Frontiers in Physiology | www.frontiersin.org 7 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis 260. The plot approximated a linear relationship (R2 = 0.6) with a 0.9 exponent. This result is more consistent with the action of a single type of motor (kinesin) mediating the transport (Kohler and Rohrbach, 2015). Uncoupling the actin cortex with cytochalasin D reduced the range of ATPves expenses to 1.3–19, and the efficiency to the lowest 0.06–0.4% range in the study (Figure 4). The small amount of exocytosis in this experimental situation suggests that only vesicles inside the cortex at the time of stimulation could fuse. This is in agreement with the 0.37–2.7 µm transport distances estimated for these clusters. The potency function that fitted these data, had again a slope of two (R2 = 0.90). These data in addition with the short transport distances points to the possibility that short filaments of actin bound to myosin and contributed to move the proximal clusters that fused. Our FIGURE 4 | Efficiency as a function of the ATPves expenses. Logarithmic plot conclusion from these sections is that the efficiency values are of the efficiency as a function of the ATPves . The thermodynamic efficiency of proportional to the ATPves expenses and may indicate additive exocytosis from peripheral clusters had a quadratic relationship with ATPves effects on the vesicle transport. expenses (green line); internal clusters (red) the relationship had a 0.9 exponent (dark red line). Uncoupling the actin cortex with cytochalasin D (blue dots) reduced the range of the relationship by two logarithmic units. Data was Velocity as a Reporter of the fitted by a quadratic potency function (black line). The equations and their significance values are presented. Thermodynamic Efficiency Figure 5 shows that the thermodynamic efficiency displayed a power law relationship with the transport velocity of the vesicles. This trend incorporated the whole population of data, although peripheral clusters traveled with a wider 15–95 nm/s range of velocities. The velocities above 60 nm/s were unreachable for internal clusters. As expected from Equation (12), the peripheral vesicles transported at higher velocities also displayed the largest -although yet low- thermodynamic efficiencies between 4.2 and 6.4%. This finding is not surprising from a different perspective: the peripheral clusters were small and had less mass to oppose to frictive obstacles. At velocities below 60 nm/s there was an extensive overlapping of both cluster populations in the chart, with the efficiencies of the internal clusters being ≤1.9%. FIGURE 5 | The efficiency depended on the transport velocity. Data from Application of the actin depolymerizing agent cytochalasin internal (red), peripheral (green) clusters, and after addition of cytochalasin D D produced a reduction in the transport velocity to 1.5– (blue) were pooled together and fitted to a potency function (black line). The equation and significance level are presented. 17.0 nm/s that correlated with the lower 0.006–0.04% range of efficiency. This result seems more related to the lack of one motor system than to an increase in the frictive forces. Data from the internal and external clusters could be fitted certain differences in the ranges of ATPves values, that are independently to potency functions with equal 1.56 exponents presented in Table 2. The transport of external clusters along and R2 values of 0.69 and 0.41, respectively. However, the the shortest 0.6 µm resting distances had a high 52 ATPves cost. pooled data set, including those data collected in the presence As the transport distance increased to 1.3 µm, the ATPves cost of cytochalasin D were best described by a single function became gradually reduced to reach minimum of 13 ATPves . As with a 1.63 slope (R2 = 0.86). This property anticipates the distance continued to increase, the trend of the energy cost that the distribution of velocities expresses effects from other reversed to reach 44 ATPves when the distance was 2.1 µm. variables such as the size of the vesicle cluster and the This was the distance at which the high-energy barrier of the cytoarchitecture of the pathway. To complement this scheme, W curve appeared. This was also the site of convergence for we have also shown that the ATPves cost also increases with the external and internal clusters. The first internal cluster rested velocity (De-Miguel et al., 2012). at 1.9 µm and release from its vesicles occurred at a high 118 ATPves cost (Figure 6A). From there, the ATPves expenses had Distance-Dependence of the ATP a second decrease to reach the second minimum, which in this Expenses case was 14 ATPves in the segment between 2.3 and 4.3 µm. The distance-dependence of the ATPves expenses reproduced The last increase complemented the W shape by reaching the the previously described W-shape (De-Miguel et al., 2012), with largest 260 ATPves value at 6.15 µm (Figure 6A). The polynomial Frontiers in Physiology | www.frontiersin.org 8 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis peripheral and internal clusters intersected. The second part of the chart had a sole contribution from internal clusters. This section could be approached by a polynomial function (R2 = 0.64). The 0.08% second minimum efficiency occurred between 2.65 and 4.30 µm, although as discussed above, data with even lower values may be missing. At 6.15 µm the efficiency reached its internal maximum value of 1.1%. Our hypothesis to explain the W-distribution of the ATPves expenses and efficiency was that each component of the plot reflects a mechanical or ultrastructural interference on the vesicle pathway. An increase in the friction can be produced by a larger number of vesicles being transported or by obstacles in the pathway. It is worth to remark that the slopes of the W chart do not refer to the behavior of the vesicles within the range of distances covering that slope but indicate the amount of ATP expenses and efficiency over their whole trip to the membrane. Following this idea, those vesicles traveling the longest distances would have to overcome the obstacles that produce each of the four slopes of the chart. These possibilities were explored in the following parts of the study. Ultrastructural Correlates of the Thermodynamic Efficiency For its susceptibility to be affected by friction forces, the number of vesicles in the clusters was our first candidate to explain the components of the W chart. The plot in Figure 6B showed that the vesicle clusters near the plasma membrane had the largest efficiencies. Figure 7 shows that those same FIGURE 6 | Distance-dependence of the ATPves expenses and thermodynamic efficiency of exocytosis. (A) The ATPves -dependence on the clusters were small, as explained in Figure 1. Intuitively, the distance had a W-shape. The short distance range of the plot contains transport of small cargos occurs with higher efficiency owing to information from peripheral (green) clusters, while distances above 1.9 µm the smaller counteracting friction forces. However, the ATPves contain information from internal (red) clusters. A maximum intermediate peak cost of the transport of these clusters was among the highest forming a high energy barrier appeared by 1.9 µm, with convergence of peripheral and internal clusters. (B) The distance-dependence of the (Figure 6A). Moreover, the relationship between the size of thermodynamic efficiency of somatic exocytosis also was W-shaped, with the clusters and the efficiency did not follow the W shape. each vesicle population separated by the intermediate maximum. The clusters The number of vesicles per cluster increased as the clusters that rested at the shortest distances had the largest efficiency values. The R2 rested more internally, to reach 930 vesicles at 4.5 µm from values are the significance of the polynomial functions fitted to the data the plasma membrane. Then the last cluster carried only 62 (black lines). vesicles with a 1.1% efficiency. This small cluster was most likely being assembled near a Golgi apparatus (see Trueta et al., 2012). This result points to elements other than the vesicle fittings in the plots had the unique intention to underscore numbers affecting the efficiency. Based on this reasoning we the W-shape distribution of the data without any use for the carried out a search for ultrastructural elements affecting the model calculations. thermodynamic efficiency. Distance-Dependence of the Ultrastructure of the Actin Cortex Thermodynamic Efficiency The dual role of the actin cortex on the vesicle transport As expected from the proportionality of the efficiency and the already described suggested its influence on the thermodynamic ATPves values in Figure 4, the thermodynamic efficiency also efficiency of the transport. The actin cortex of neurons stimulated displayed a W-shape dependence on the transport distance with 1 Hz trains of impulses was stained with phalloidin coupled (Figure 6B). The distance ranges of the efficiency plots were to Alexa fluorescent dye. The fluorescent label in equatorial the same as for the ATP expenses. However, the efficiency of images of the soma consisted of a thick 1.93 ± 0.74 µm (S.D.) peripheral clusters covered a larger range of values than that of array of radial bundles (Figure 8), as quantified from 46 counts internal clusters. The first polynomial distribution in Figure 6B of different parts of the cortex of five neurons. This thickness was included the data from peripheral clusters (R2 = 0.84). The similar to the distance at which we found the high energy barrier low distance extreme had the higher 6.4% efficiency. At deeper and high efficiency intermediate peak of the W distributions distances the values first decreased to a 1.9% minimum and shown in Figure 6. Such value gives a possible explanation to the then increased to reach the intermediate 1.4% peak right where third slope of the W distributions in Figure 6. As internal clusters Frontiers in Physiology | www.frontiersin.org 9 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis Distribution of Endoplasmic Reticulum The search for alternative ultrastructural candidates to explain the ATPves expenses and thermodynamic efficiency of the first half of the W distributions took us to the endoplasmic reticulum. Electron micrographs showing release sites of neurons were obtained by fixing neurons right after 1 Hz stimulation (n = 5) to maintain the resting ultrastructure of the transport pathway (Trueta et al., 2004). The images in Figure 9 contain structures immersed in the actin cortex, although the conventional fixation technique that we used to prepare the sections does not allow to resolve its structure. Figure 9A contains a cluster of electrodense vesicles resting distantly from the plasma membrane. Subsequent vesicles are bound by small fine filaments. The vesicle cluster was bound indirectly to the plasma membrane via a thick bundle of microtubules, according to the diameter of the individual fibers. FIGURE 7 | Distance-dependence of the number of vesicles that fused per Single vesicles appeared along the microtubules, presumably cluster. The number of vesicles in the clusters increased with the distance from on their way to the plasma membrane (Leon-Pinzon et al., the plasma membrane. The most internal clusters were small. Peripheral clusters are represented in green and internal in red. 2014; Figure 1). As explained in Figure 1, this vesicle migration explains the reduction of the number of vesicles as the peripheral clusters rest closer to the plasma membrane. An alignment of endoplasmic reticulum bags bordered the intracellular side of the plasma membrane; deeper and smaller bags of endoplasmic reticulum were scattered between the vesicles and the plasma membrane. One may wonder that vesicles being transported to the plasma membrane will find these bags on their way forming a bottleneck. Electron micrographs obtained from neurons fixed after 20 Hz stimulation confirmed this idea. The image in Figure 9B shows vesicles from a large cluster reaching the plasma membrane by passing between endoplasmic reticulum. These obstacles bottlenecked the flux of vesicles and can be considered as sources of friction forces that reduce the thermodynamic efficiency of somatic exocytosis. Countings of the distance between the plasma membrane and the center of mass of endoplasmic reticulum bags are presented in Figure 9C. The green and red lines fit the data distribution to two Gaussians, one with a mean 0.36 ± 0.11 µm (SD) distance from the plasma membrane, corresponding to the more external layer of endoplasmic reticulum. The red line fits the distribution of the scattered internal bags of FIGURE 8 | Actin cortex of Retzius neurons. Confocal equatorial image of the endoplasmic reticulum, rendering a mean 0.93 ± 0.12 µm soma of a Retzius neuron showing the fluorescence of Alexa dye coupled to distance. This distribution supports that the endoplasmic phalloidin. The perinuclear region and primary axon also display a profuse reticulum is a source of friction forces that reduce the staining. n indicates the position of the nucleus. thermodynamic efficiency. Smaller vesicle clusters facing the plasma membrane seem to rest between the external layer of endoplasmic reticulum in absence of further obstacles to reach the plasma membrane. rested closer to the high energy barrier increasing amounts of vesicles were inside the actin cortex, where the myosin carried by the clusters assembles the actin-myosin transport Multiple Variables Affect the with the actin filaments (Noguez et al., in preparation). As Thermodynamic Efficiency larger fraction of the clusters added the myosin-actin dymers The multivariable schemes in Figure 10 integrate the data on the to the kinesin-tubulin transport, the cost and efficiency of the possible variables that determine the thermodynamic efficiency transport would increase. However, this is a partial explanation. of somatic exocytosis. Each element of the transport pathway has A fuller account comes from the origins of the two short been scaled based on the experimental evidence. The diameter distance slopes of the W charts, which are explained in the of the circles representing each cluster was calculated from following paragraphs. its number of vesicles. Peripheral clusters are organized in an Frontiers in Physiology | www.frontiersin.org 10 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis FIGURE 9 | Distribution of smooth endoplasmic reticulum in the soma shell. (A) Electron micrograph of a neuron that had been stimulated at 1 Hz. Vesicles remain at their resting states. A somatic vesicle cluster (vc) is bound to the membrane (pm) via a bundle of cytoskeletal fibers, most likely microtubules (mt). Peripheral endoplasmic bags (er) rest closely apposed to the plasma membrane. More internally, another layer of endoplasmic reticulum (er) contains smaller bags. Individual vesicles (v) can be seen in an apparent migration to the membrane, along the microtubule bundles (see also Figure 1). Glial cell processes (g) in an invagination of the Retzius neuron, right at the anchor site of microtubules to the plasma membrane. (B) Electron micrograph of a release site in a neuron that had been stimulated with 20 Hz trains. Vesicles in a large cluster are apposed to the membrane. Transport occurs through a bottleneck of endoplasmic reticulum. Mitochondria (mit) are common satellites of the clusters that travel with them. Multi-vesicular bodies (mvb) result from the incorporation of vesicles after exo/endocytosis (Trueta et al., 2012). Note that exocytosis occurs onto the glia. (C) Distribution of endoplasmic reticulum in the soma shell. The distances have the plasma membrane as reference. Peripheral (er) and internal (er) pools of endoplasmic reticulum were distinguished by Gaussian fittings to the histograms. The mean values for each distribution are indicated. ascending order of efficiency. The distance from the plasma and ultrastructural interactions. Both regions in which the membrane to the center of mass of the clusters was determined ATP hydrolysis and efficiency had increasing slopes also had by the model fittings. Pairs of clusters releasing in the same higher transport velocities. On the contrary, the regions in spot are associated by a black line representing the microtubule which the energy and efficiency had decreasing trends had bundles. The efficiency of the ATP expenses per vesicle is slower velocity ranges. This result, which can be predicted indicated in the center of each cluster; the velocity of the from the formula of the thermodynamic efficiency in Equation transport is indicated on the right of each cluster. The actin (12), acquires a morphological correlate in Figure 10. Table 3 cortex and endoplasmic reticulum are represented according summarizes the data according to the groups of vesicle clusters. to the morphometric analysis descried above. At first glance For the small peripheral clusters in Group 1, the additive there is a good correlation between the size, the resting distance action of two motors and the clusters resting already between and the efficiency of peripheral clusters. The thermodynamic endoplasmic reticulum in the more peripheral layer may favor efficiency of the exocytosis process from vesicles in these higher velocities and efficiencies at the expenses of the high peripheral clusters was inversely proportional to their resting ATPves cost. Group II has two friction barriers represented by distance. Similar correlations are unclear for the internal clusters the two layers of endoplasmic reticulum. As vesicles enter the in this representation, because although they were associated barriers the thermodynamic efficiency decreases. This can be to a peripheral cluster, their biophysical properties were not attributed to the friction exerted by the endoplasmic reticulum correlated. The correlations between different variables of the on the vesicle clusters. In group III, the large clusters are at clusters and the ultrastructure of the transport pathway are least in part, immersed in the actin cortex. The assembly of simplified in Figure 10B. The vesicle clusters were grouped two motors may increase the ATP expenses and efficiency. from I to IV based on the distance, efficiency, size, velocity, However, the effect of the endoplasmic reticulum barriers is Frontiers in Physiology | www.frontiersin.org 11 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis FIGURE 10 | Structural and biophysical correlations of the thermodynamic efficiency of the ATPves hydrolysis. (A) Pairs formed by peripheral (green circles) and internal (red circles) vesicle clusters that discharged in the same site are represented attached to microtubules (black lines). The distances were calculated by the model fittings from the mass center of the cluster to the plasma membrane. The diameter of the clusters corresponds to the number of vesicles in the cluster. For each cluster, the red numbers inside indicate the efficiency (%), and the black numbers on the right the transport velocity (nm/sec). The peripheral clusters are presented from bottom to top according to their increasingly efficiency values. Their paired internal clusters had independent efficiency values, velocities, sizes and traveling distances. The actin cortex is represented in pale orange. Both layers of endoplasmic reticulum, one immediately inside the plasma membrane (er1 ) and the other ∼1 µm inside (er2 ) are represented as pale sacs. The number of vesicles decreased as the clusters approached the plasma membrane. The efficiency of the peripheral clusters decreased as the distance increased. The number of vesicles, the efficiency, the transport distance and velocity of their corresponding internal clusters were uncorrelated with those of their peripheral pairs. (B) Vesicle clusters were groped according to their efficiency, size, distance, and velocity. The thermodynamic efficiency of somatic exocytosis also correlated with the thickness of the actin cortex (pale orange) and both subsequent layers of endoplasmic reticulum (gray bars). Group I contains the smallest and more peripheral clusters, which also had the highest thermodynamic efficiency values. These clusters rested at the entrance of the submembrane barrier of endoplasmic reticulum (gray bar adjacent to the plasma membrane). Group II contained clusters embedded within the second layer of endoplasmic reticulum, (more internal gray bar). The transport velocities and efficiencies of these clusters were smaller than those of Group I. Group III (brown) rested in the limits of the actin cortex. These clusters were large, moved with high velocity and their efficiencies were above 1%. Group IV (red) contained large internal clusters that rested inside the actin cortex. Their velocities were smaller than those in Group III. The smaller cluster was the deeper (gray arrowhead). This cluster did not correlate with the rest of group IV for its size and for having a relatively large 1.1 efficiency, in spite of its low 26 nm/s velocity. Its size and position suggest that it was in the assembly process at the time of the stimulation series. diminished. This can be explained if the flow of the peripheral DISCUSSION clusters that precede the larger internal clusters has already diminished the friction forces by displacing the endoplasmic The application of thermodynamic theory to the study of somatic reticulum to the side, thus widening the spaces though which exocytosis predicts how the cytoarchitecture of the vesicle the internal clusters will flow. If so, the pairing of clusters trafficking pathway influences the cost and thermodynamic in the same microtubule pathway would favor the transport efficiency of serotonin release. In spite of the common belief that of the internal larger vesicle clusters. The ATP expenses and biological systems operate with high efficiency levels, somatic thermodynamic efficiency of vesicles in Group IV may stem from exocytosis is far from an ideal system. Isolated myosin motors moving on actin fibers have efficiencies of 45% (Kjelstrup et al., their longer traveling distance, part of which is solely covered 2013). Therefore, the low efficiency reported here shows the by the force of kinesin motors. In addition, entering the actin additive effects of the low efficiency of the motors and the frictive cortex may impose friction forces due to the accommodation effects imposed by the ultrastructure of the transport pathway. of the vesicles within the entanglement of the actin fibers, Surprisingly, the thermodynamic efficiency of the simple calcium before the coupling of the myosin motors. Another group ATPase immersed in the plasma membrane, depends on the lipid that can be predicted contains the small clusters that are composition of the membrane, with low efficiency values ≤12% assembled and transported from the parikaryon (see Trueta (Lervik et al., 2012). Therefore, the values estimated here seem et al., 2012). However, more evidence is required to strengthen reasonable by considering the number of variables affecting the this argument. vesicle transport. Frontiers in Physiology | www.frontiersin.org 12 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis TABLE 3 | Variables contributing to the energy cost and efficiency of somatic exocytosis. Cluster group I II III IV Distance to membrane (µm) 0.6–1.1 1.0–2.3 1.8–2.6 2.7–6.1 Efficiency (0%) 1.0–6.4 0.2–0.6 0.7–2.0 1.1 ATPves 27–45 11–43 28–260 13–30 Velocity nm/s 45–95 12–30 60–71 35–12 Size of cluster Small Intermediate Large Larger Vesicles per cluster 95–169 174–260 229–641 262–930 (65) (52) Intracellular structures Actin cortex, Actin cortex, Actin cortex interface Cytoplasm Endoplasmic Endoplasmic Endoplasmic Actin cortex interface reticulum 1 reticulum 1+2 reticulum 1+2 Endoplasmic reticulum 1+2 Transport system Kinesin Kinesin Kinesin Kinesin Myosin Myosin Some Myosin Later Myosin The red numbers correspond to the decreasing slopes of the W distributions of ATPves expenses and efficiency; the blue numbers correspond to the increasing slopes of the W distribution. Other colors underscore different structures; the tones indicate gradations. The number of vesicles in parenthesis are out of range. The value in Group IV corresponds to the most internal cluster, most likely under formation at the time of the stimulation of exocytosis. Endoplasmic reticulum 1 and 2 correspond to the external and internal layers in Figures 9, 10, respectively. It is pertinent to discuss a potential source of error in our vesicles with a particular building block of the exocytosis process. measurements. The reports of the rate constant values of the The same structures that regulate the exocytosis machinery ATP cleavage that fuels the actin and myosin motors have hamper the thermodynamic efficiency of the transport. For considerable variations depending on the subtype of motor example, the endoplasmic reticulum is the fundamental source and the experimental conditions of the measurements. Since for intracellular calcium that first activates the vesicle transport these variations span over similar ranges 100–300 s−1 , we could in response to high frequency stimulation (Trueta et al., 2004), choose one single value to represent both rate constants for our and later maintains the large-scale exocytosis in response to the calculations. The choice for the low 100 s−1 value seemed the activation of serotonin autoreceptors (Leon-Pinzon et al., 2014). most accurate for our purposes, because the 18◦ C temperature In a previous study (Trueta et al., 2004) we have shown that very at which our experiments were carried out—leeches are cold large vesicle clusters become apposed to the plasma membrane blooded animals—decreases the rate constants of chemical in response to electrical stimulation. This observation implies processes. We have no way to justify that this choice reflects the that they occupy positions that at rest contained endoplasmic real values with which the vesicle transport operates in Retzius reticulum. The endoplasmic reticulum may then be moved neurons since their motor subtypes are only superficially known. aside during transport of the peripheral vesicle cluster. As Antibodies against myosin type IV succeeded to bind myosin in a positive consequence, the internal cluster that follows the other set of experiments and the contribution of each motor to same trajectory may find a cleared pathway to the plasma somatic exocytosis has been blocked pharmacologically (Noguez membrane, with a concomitant saving of energy and reduced et al., in preparation), but we still lack estimates of their rate heat dissipation. constants. If the rate constant values were higher, the estimate The actin cortex adds another duality to neurons and excitable of the efficiency would decrease linearly in proportion to the endocrine cells by preventing the entry of the vesicle clusters increase in the rate constant values, as predicted from Equation at rest and by propelling vesicles in response to electrical (12). For example, a 20% increase in the rate constant value stimulation (Vitale et al., 1995; Lang et al., 2000; Oheim and from 100 to 125 s−1 would reduce the efficiency from 6.0 to Stühmer, 2000; Giner et al., 2005; Tobin and Ludwig, 2007; 4.8%; likewise, a 200% increase in the rate constant value to Gutiérrez and Gil, 2011; Torregrosa-Hetland et al., 2011). The 300 s−1 -which is near the largest estimate available (Johnson third player is mitochondria, the fuel generator that in response and Taylor, 1978; Apell et al., 1996; Higuchi et al., 1997; De La to calcium produces ATP that activates the motors. Mitochondria Cruz et al., 1999; Cross, 2004; De la Cruz and Ostap, 2009)- travel along with the vesicle clusters, as suspected because both would reduce the efficiency to 0.2%. In any case, the values organelles appear together in electron micrographs after 1 or would move downwards linearly but not logarithmically. The 20 Hz stimulation. The cargo imposed by the mitochondria additional possibility that each motor operates with a different may be as large as, or even larger than that imposed by rate constant value cannot be resolved with the tools of our study. the cluster of vesicles. Therefore, it is most likely that the The measures of the average velocity of the transport normalize mobilization of the energy generators along with the vesicle these possible variations without sensitivity to separate them. clusters increases the friction forces at the expenses of the A duality has emerged between the structure/function thermodynamic efficiency. relationship of the release sites and the thermodynamic efficiency A final question from our study concerns its general of somatic exocytosis. Each slope of the W distribution of the significance. Somatic exocytosis is part of a wider communication efficiency vs. distance plot is influenced by the interaction of complex system that involves not only the soma, but every part Frontiers in Physiology | www.frontiersin.org 13 May 2019 | Volume 10 | Article 473 Noguez et al. Thermodynamic Efficiency of Somatic Exocytosis of the neuron. A remarkably similar mechanism for somato- AUTHOR CONTRIBUTIONS dendritic exocytosis has been demonstrated in thalamic neurons releasing the peptides vasopressin and oxytocin PN and FD-M designed and carried out the experiments, (Ludwig and Stern, 2015). Moreover, the mobilization of conducted the analysis and prepared the figures. MR designed the serotonin-containing exocytosis structures in the isolated mathematical approach. FD-M wrote the manuscript. soma of Raphe neurons from mammals follow similar steps (Sarkar et al., 2012). The soma and dendrites of thalamic FUNDING neurons releasing peptides contain an actin cortex whose activation promotes the vesicle transport and exocytosis Our work was funded by a Dirección General de Asuntos (Tobin and Ludwig, 2007). The ATP expenses and efficiency del Personal Académico (DGAPA) grant IN210317 from of exocytosis have not been explored in those or in other the Universidad Nacional Autónoma de México (UNAM) types of neurons, but the highly conserved mechanism of and grant 130031 from the Consejo Nacional de Ciencia somatic and in general extrasynaptic exocytosis (Trueta y Tecnología (CONACyT) to FD-M. MR was supported et al., 2012) suggest that the effects presented here may be of by MINECO of the Spanish Government under grant Fis general interest. The dendrites and small axon varicosities, 2015-67837-P. PN is a doctoral student from Programa de for example release of serotonin through a mechanism Doctorado en Ciencias Biomédicas, Universidad Nacional similar to that in the soma, although the transport distances Autónoma de México (UNAM) and received fellowship 193987 of the vesicles are downscaled. The ATP expenses and the from CONACYT. thermodynamic efficiency of the vesicle transport for their exocytosis may be scaled accordingly. Such smaller traveling ACKNOWLEDGMENTS distances may require less ATP and may operate with higher thermodynamic efficiencies. We wish to express our gratitude to Mr. Bruno Mendez Ambrosio The mechanism for somatic exocytosis seems to be his excellent technical assistance during this study, and to Mrs. highly conserved also for most signaling molecules in Sara Flores González for her invaluable assistance in the animal the central and peripheral nervous system (For review and laboratory care. We also express our gratitude to Mr. see Trueta and De-Miguel, 2012; Del-Bel and De-Miguel, Francisco Perez for his continuous support in the computer 2018). Secretory cells follow similar mechanistic rules by unit and to Mr. Rodlfo Paredes and Dr. Fernando García transporting vesicles across an actin cortex in response to Hernandez for their invaluable help in the preparation el the stimulation (Vitale et al., 1995; Lang et al., 2000; Oheim electron micrographs and fluorescence microscopy. The animal and Stühmer, 2000; Giner et al., 2005; Gutiérrez and Gil, care facility at our Institute was fundamental for the good 2011; Torregrosa-Hetland et al., 2011). These arguments conditions of our animal colony. Professor J. G. Nicholls, Dr. suggest that our results represent general mechanisms Sharlen Moore, and Mrs. Sorel Achouna made critical readings in biology. of our manuscript. REFERENCES De Groot, S. R., and Mazur, P. (1969). “Chapter 7,” in Non-equilibrium Thermodynamics (New York, NY: Dover Publications Inc.), p. 510. Alberty, R. A., and Goldberg, R. N. (1992). Standard thermodynamic De la Cruz, E. M., and Ostap, E. M. (2009). 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Interactions No use, distribution or reproduction is permitted which does not comply with these between mitochondrial bioenergetics and cytoplasmic calcium in cultured terms. Frontiers in Physiology | www.frontiersin.org 15 May 2019 | Volume 10 | Article 473